An Interpretation of Crs Attributes of Time-migrated Reflections

Applied to unmigrated data, the Common-Reflection-Surface (CRS) method is able to produce high-quality stacked sections, as well as useful traveltime parameters for a number of imaging and inversion purposes. One difficulty of the CRS method is the treatment of diffractions, especially when located close to reflections, and also triplications. In these regions, the CRS parameters obtained by coherence-measure procedures become inaccurate. In this context, and also for more general reasons, it might be interesting to investigate the use of the CRS methodology in the time-migrated domain, where diffractions have been collapsed and triplications untangled. The CRS method applied to the time-migrated domain approximates the zero-offset reflection traveltime as a second-order Taylor expansion in image point coordinates, in the vicinity of a given image ray. It is to be remarked the analogy to the conventional CRS application to the unmigrated, poststack domain, in which the zero-offset reflection traveltime is approximated as a second-order Taylor expansion in midpoint coordinates, in the vicinity of a given normal ray. Based on pioneering work of the mid eighties at NORSAR, we use the methodology of surface-to-surface propagator matrices for anisotropic media and obtain expressions that relate reflector dip and curvature to first and second derivatives of the time-migration reflection time with respect to image point coordinates. This provides an interpretation of the CRS coefficients. Besides its intrinsic interest, such quantitative relationships can provide useful constraints for the construction of selected reflectors from interpreted reflection events in the time-migrated domain.